With a simple majority of 22 votes required for victory, Cookson now has pledges from Europe and Oceania and further support from North America. McQuaid can likely count on votes from Africa and Asia.
Cookson, the longtime British Cycling president, is pledging to rebuild cycling's image and governance after the Lance Armstrong doping affair.
McQuaid is seeking a third four-year term amid widespread criticism of the Irish official and UCI's handling of doping allegations.
It remains unclear if McQuaid has a valid nomination to be a candidate. Federations in his home country Ireland and Switzerland, where he lives, withdrew support.
McQuaid claims valid nominations from Thailand and Morocco, but those would only be legitimate if amendments to UCI rules are passed in a vote in Florence.
Malaysia wants to retroactively allow any two federations to propose a candidate. Barbados and Turkey suggest that incumbent presidents should have an automatic right to stand for re-election.
Still, European delegates also voted Sunday to oppose late rules changes at the election congress.
"I am also very pleased that the UEC has voted so strongly against amending the rules of the election retrospectively," Cookson said.
Cookson pledged that, even if he was the only candidate eligible on election day, he would accept the presidency only if he achieved the majority of 22 votes.